Question

A survey finds that a 95%confidence interval for the mean salary of a police patrol officer in Fresno, california, in 2016 is $52,516 to $53,509. A student is surprised that so few police officers make more or less that $53,500. Explain what is wrong with the student’s interpretation.

Answer 1

We have a sample from a population of all the police patrol officers in Fresno, California, in 2016. We know the mean of a sample and we build an interval which covers the mean of a population a with the probability $\gamma=0.95$ (95% confidence interval).

$(52.516,53.509)$ --- 95% confidence interval.

$52.516<a<53.509$

But a may turn out to be outside of this interval with the probability 0.05.